I think you should attempt to retain everyone. Option 2 for a low performer sounds better to me: “The other path is document the violation and give an opportunity to improve”.

A few months into one of my first jobs after college I was given a stern lecture from my manager “we don’t mind you leaving early on Friday if your work is getting done, but it’s not”. That was the wake up call I needed and I worked for the company for another 8 years, becoming, I’d like to think, a valuable high performer.

If they remain a low performer, then that’s another story…